Vieta's formulas
Write a Quadratic Equation When Given Its Solutions
If $x}_{1$ and $x}_{2$ are the roots of the quadratic equation $\mathrm{ax}}^{2}+\mathrm{b}x+\mathrm{c$ = $0$ then:
${x}_{1}+{x}_{2}$ = $-\frac{b}{a}$
$x}_{1}\hspace{0.17em}\xb7\hspace{0.17em}{x}_{2$ = $\frac{c}{a}$
If $x}_{1$ and $x}_{2$ are the roots of the quadratic equation ${x}^{2}+px+q$ = $0$ then:
${x}_{1}+{x}_{2}$ = $-p$
$x}_{1}\hspace{0.17em}\xb7\hspace{0.17em}{x}_{2$ = $q$
Write a Cubic Equation When Given Its Solutions
If $x}_{1$, $x}_{2$ and $x}_{3$ are the roots of the cubic equation $\displaystyle a{x}^{3}+b{x}^{2}+cx+d$ = $0$ then:
$x}_{1}+{x}_{2}+{x}_{3$ = $-\frac{b}{a}$
$x}_{1}{x}_{2}+{x}_{1}{x}_{3}+{x}_{2}{x}_{3$ = $\frac{c}{a}$
$x}_{1}\hspace{0.17em}\xb7\hspace{0.17em}{x}_{2}\hspace{0.17em}\xb7\hspace{0.17em}{x}_{3$ = $-\frac{d}{a}$